Motivated by applications such as the spread of epidemics and the propagation of influence in social networks, we propose a formal model for analyzing the dynamics of such networks. Our model is a stochastic version of discrete dynamical systems. Using this model, we formulate and study the computational complexity of two fundamental problems (called reachability and predecessor existence problems) which arise in the context of social networks. We also point out the implications of our results on other computational models such as Hopfield networks, communicating finite state machines and systolic arrays.

Subjects: 9.2 Computational Complexity; 9.3 Mathematical Foundations

Submitted: Oct 16, 2006

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